The Titanite Slab in Royal Wood can be obtained from the chest behind the waterfall either after Black Dragon Kalameet is defeated or even before, if you're fast enough. It's in a chest behind the larger waterfall on the right, that you see in front of you when you are standing at the top of the ladder, looking directly across the valley. You can run quickly across the valley and through the waterfall before Kalameet gets to you, open the chest and take the slab, then use a Homeward Bone/Homeward to leave. It is even possible to return to the ladder and escape without taking damage if you stick to the edge of the arena.